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Low Reynolds numbers flow past an ellipsoid of revolution of large aspect ratio

Published online by Cambridge University Press:  28 March 2006

Yun-Yuan Shi
Yun-Yuan Shi
Affiliation:
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, California
Now at Porter Hall, Carnegie Institute of Technology, Pittsburgh, 13, Pennsylvania, U.S.A.
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Abstract

The results of Proudman & Pearson (1957) and Kaplun & Lagerstrom (1957) for a sphere and a cylinder are generalized to study an ellipsoid of revolution of large aspect ratio with its axis of revolution perpendicular to the uniform flow at infinity. The limiting case, where the Reynolds number based on the minor axis of the ellipsoid is small while the other Reynolds number based on the major axis is fixed, is studied. The following points are deduced: (1) although the body is three-dimensional the expansion is in inverse power of the logarithm of the Reynolds number as the case of a two-dimensional circular cylinder; (2) the existence of the ends and the variation of the diameter along the axis of revolution have no effect on the drag to the first order; (3) a formula for drag is obtained to higher order.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 23 , Issue 4 , December 1965 , pp. 657 - 671
Copyright
© 1965 Cambridge University Press

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References

Breach, D. R. 1961 Slow viscous flow past ellipsoids of revolutions. J. Fluid Mech., 10, 306–14.Google Scholar
Cole, J. D. & Roshko, A. 1954 Heat transfer from wires at Reynolds numbers in the Oseen range. Heat transf. & Fluid Mech. Inst.
Erdelyi, E. 1953 Higher Transcendental Functions. New York: McGraw-Hill.
Kaplun, S. 1957 Low Reynolds number flow past a circular cylinder. J. Math. Mech., 6, 595–603.Google Scholar
Kaplun, S. & Lagerstrom, P. A. 1957 Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers. J. Math. Mech. 6, 585–93.Google Scholar
Lagerstrom, P. A. 1956 Higher Speed Aerodynamics and Jet Propulsion, Laminar Flow and Transition to Turbulence. Princeton Series (to be published).
Lagerstrom, P. A. & Cole, J. D. 1955 Examples illustrating expansion procedures for Navier-Stokes equations. J. Rat. Mech. 4, 817–882.Google Scholar
Lamb, H. 1932 Hydrodynamics. New York: Dover.
Oberbeck, A. 1876 J. reine & angew. Math. 81, 62–80.
Oseen, C. W. 1927 Neuere Method und Ergebnisse in der Hydrodynamic. Leipzig: Akad. Verlagsgesellschaft.
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds number for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237.Google Scholar
Shi, Y. Y. 1963 Low Reynolds number flow past finite cylinder of large aspect ratio. Ph.D. Thesis, Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, California.